In this paper, we present a novel diffusion model-based monaural speech enhancement method. Our approach incorporates the separate estimation of speech spectra's magnitude and phase in two diffusion networks. Throughout the diffusion process, noise clips from real-world noise interferences are added gradually to the clean speech spectra and a noise-aware reverse process is proposed to learn how to generate both clean speech spectra and noise spectra. Furthermore, to fully leverage the intrinsic relationship between magnitude and phase, we introduce a complex-cycle-consistent (CCC) mechanism that uses the estimated magnitude to map the phase, and vice versa. We implement this algorithm within a phase-aware speech enhancement diffusion model (SEDM). We conduct extensive experiments on public datasets to demonstrate the effectiveness of our method, highlighting the significant benefits of exploiting the intrinsic relationship between phase and magnitude information to enhance speech. The comparison to conventional diffusion models demonstrates the superiority of SEDM.